Bibliographic record
Abstract
With machine learning gaining increasing popularity in recent years, most successes from employing machine learning methods are found in the fields where the problem solving relies heavily on pattern recognition and representation learning, with solutions consisting of sophisticated rules and logic that cannot be expressed by concise mathematical descriptions. Such fields of study include computer vision, natural language processing, molecular biology, and so on. On the other hand, in the field of mathematical optimization, the common nature of the problems is drastically different: each optimization problem is entirely formulated by highly abstract closed-form mathematical concepts. Therefore, machine learning is seemingly unfit for being a universal tool to mathematical optimizations. While there have been attempts on using machine learning for mathematical optimizations, the majority of the solutions developed in the literature are essentially problem-specific black box models learning existing input-to-solution mappings via brute force data-fitting. Furthermore, many such works only exploit machine learning as computationally faster alternatives or complementary pieces to the conventional mathematical algorithms. In this dissertation, we propose novel and generalizable machine learning approaches, each of which effectively solves a class of mathematical optimization problems, with benefits beyond just having faster or complementary computations. Specifically, we elaborate on three research projects along this direction: the uncertainty injection approach for robust optimizations; the transfer learning with reconstruction loss approach for solving correlated optimization tasks sharing the same input distribution; and the generalization of optimal control and reinforcement learning for non-cumulative objectives, where the proposed generalizations are over both the problem formulations and the corresponding algorithms. Throughout this dissertation, each of the proposed machine learning approaches is designed to be generalizable, flexible, and not restricted to any specific problem or application setting. Each approach serves more than just being a substitution to any existing mathematical optimization algorithm. We hope this dissertation is able to unveil the true potential of machine learning for being an imperative option when it comes to tackling general mathematical optimization problems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".